Rewrite as a simplified fraction. ${2.67\overline{2} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2672.2222...\\ 100x &= 267.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2405}$ ${x = \dfrac{2405}{900}} $ ${x = \dfrac{481}{180}} \text{or} {2 \dfrac{121}{180}}$